The US Vice President Mike Pence has praised his "productive" meeting with Deputy Prime Minister Winston Peters at the White House.

In an image posted to Mr Pence's Twitter page, Mr Peters can be seen seated next to the US Vice President, as the pair discussed improving bilateral trade and "deepening cooperation on shared goals that benefit both countries".

Mr Peters left New Zealand for the US last week to meet with Mr Pence, the Secretary of State Mike Pompeo and other senior members of the Trump administration including the Director of National Intelligence Dan Coats and National Security Adviser John Bolton.

A spokesperson said Secretary Pompeo thanked Mr Peters for New Zealand's "continued support in working towards the final, fully verified denuclearisation of North Korea" as well as New Zealand's "assistance in countering terrorism in Iraq and Afghanistan".

Mr Peters told RadioLIVE from the US on Tuesday his discussion with Mr Pence was "beyond what we could have hoped for", adding that topics included security and trade connections.

He said he won't speculate as to where the meeting could lead to, but said the US has made it "very clear" that it's "interested in bilateral relationships in trade when people respect the common rules of law and free trade".

Mr Pence, known to be ultra-conservative, was a "personal figure" and "very influential", according to Mr Peters.

"In the end, you take the personality that you're dealing with, and endeavour to get the best you possibly can between two countries... And that's where we got to," Mr Peters said when asked about Mr Pence's personality.

Over the weekend Mr Peters called on the Trump administration to engage more with the Pacific and to provide more aid for the region, during a speech at Georgetown University in Washington, DC.

"We share a special connection for we both retain democratic traditions that have stood firm despite the upheavals of the twentieth century," Mr Peters said, declaring that there are "few relationships better than that between New Zealand and the United States".

His speech took a turn when he "unashamedly" asked the US to "engage more" in the Pacific, saying it would be in its "vital interests" to do so with US territories in the region including American Samoa, Guam, and the Northern Marianas.

New Zealand is the second biggest developed donor for the Pacific region behind Australia which accounts for 40 percent.

Mr Peters in May set aside $714 million in aid over the next four years for the Pacific, and said New Zealanders should understand that future economic and security issues will be governed by it. There was speculation it was an attempt to combat Chinese influence.

Mr Peters said in his speech that large players are showing interest in the Pacific, although he did not mention these large players by name. He said the "speed and intensity of those interests at play are of great concern to us".

The Deputy PM's trip to the US comes after Prime Minister Jacinda Ardern met Mr Pence at the East Asia Summit in Singapore last month. She sat next to Mr Pence and his wife, Karen, at the gala dinner for world leaders.

While Mr Pence requested to sit next to Ms Ardern at the dinner, she was unable to secure an exemption for New Zealand on US tariffs on steel and aluminium, as Australia has done.